Have to say, I’m not surprised to hear that readings sometimes fluctuate with the monitor. I’m more surprised that they don’t fluctuate with smart meter too.
For example, an electrically operated divertor valve in the central heating might choose the same moment to flip off or on, or the boiler may trigger itself of/on, or its flu extractor fan. Or a bathroom fan might switch itself off, if you’d been in that room recently. Or the neighbour’s cat might trigger a security light, or some rechargeable device (phone, whatever) may become fully charged and trigger its charger ‘off’. Let alone the fridge thermostat which could make a huge difference, or a PC may start downloading software updates, or an incoming email might cause a disc to spin up, and so on, and on....
Personally, for easily definable items like lights bulbs, I just look at the product label. If a bulb says 60W, or 5W, whatever then that’s what it is. I have double checked a few with stand alone metering, always been near 100% accurate, despite some urban myths reported in certain newspapers.